Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mathematical Physics

  1. Nov 13, 2007 #1
    Hi, I am a grade 12 student living in Canada and I am very interested in theoretical physics. I am currently leaning towards doing a mathematical physics program at Waterloo for my undergraduate, however I'm not yet completely sure..:

    1) Should I consider doing just a physics program? What are the real differences between mathematical physics and physics? (the reason mathematical physics appeals to me more is because I have heard it was what one would take in preparation for doing theoretical work in graduate, plus I enjoy doing math more than lab work)

    2) What is the best university in Canada for such programs? I am very ambitious so I want to go to the most reputable school in order for me to then be able to do my graduate outside of Canada. Waterloo is my first choice at the moment because I hear it's the best school for math, however I don't like the fact that I would have to take computer science courses in my first year, which doesn't seem to be the case for other universities such as U of T.
  2. jcsd
  3. Nov 13, 2007 #2
    1) you can typically take math courses taken by math majors while participating in the labs for your science courses. you don't really have to choose until you've finished your first year

    2) both waterloo and u of t are good schools. to be frank i doubt there'd be that big of a difference for the most part for the programs you're looking at. what really sets the two schools apart is LOCATION. think long and hard, make sure that you're willing to live in waterloo (or toronto, or anywhere else) for four-five years before you make any commitments

    good luck!
  4. Nov 13, 2007 #3
    That sounds like good motivation for choosing the mathematical physics option.

    This requirement strikes me as a really good idea, actually.
  5. Nov 13, 2007 #4
    for uw, you only need to take CS courses if you do mathematical physics through the math faculty. There is an identical program offered through the faculty of science that doesn't have the CS requirement.
  6. Nov 13, 2007 #5


    User Avatar

    The CS requirement is a great idea; knowing at least basic programming is an essential tool in just about every area of physics.
  7. Nov 13, 2007 #6
    If you want to be a theoretician you will need to know the math anyway so it wouldn't hurt you at all. You just might want to make sure taking it doesnt sacrafice any more practical/experimental physics courses that you might want to take. And taking some sort of math/physics program isn't required to do theoretical physics in grad school.

    Most any good school in Canada (McGill, UofT, UBC, UW, Queens...) will get you where ever you want to go provided you put in the work. Where mathematical physics, specifically, is concerned, the schools you are considering, UofT and UW, would be good choices. It really just comes down to which school you want to spend 4-5 years of your life at. UofT is a huge urban school with a commuter population and large classes, UW is a lot smaller.

    Regarding the computer science, I wish my school (UBC) forced me to take it in first year (though they force us to take it in 2nd year, which you may want to check into at UofT). You will need to learn some programming language at some point in your life, and any work you do with researchers as an undergrad will likely involve you doing some programming. It is an essential skill to have.
    Last edited: Nov 13, 2007
  8. Nov 13, 2007 #7
    If you want to pursue Mathematical Physics, you will need to learn to like computers.
    I'm not saying the one or 2 comp sci classes required will be amazingly beneficial, but eventually if you are doing Theoretical Physics (Mathematical Physics) you will need to be able to have computers do simulations for you. You won't necessarily need to be an amazing programmer, but I'm sure you'll have your fair share of programming to do.

    You also probably will have to do some labs as an undergrad. I wouldn't think there's an undergrad track offered that requires absolutely no lab work. I'm currently doing a Theo Physics/ Applied Maths major. I'm required to do less lab work than the General Physics majors, but less lab work is not zero in my case. I had 2 semesters of lab for the first year and one for my second year, then that was the only requirement. I may take another semester of Electronics lab just because I find it interesting.

    Also in my Math classes, we use programs like Maple. Its not the same as coding in C or Java, but if you are dreading all things computer science then good luck with Maple or Matlab or Mathematica.
  9. Nov 14, 2007 #8
    Lab work is as essential to a theorist as theory is to an experimentalist. Nobody is going to care about your theories if there is absolutely no way to test them experimentally.

    You still need to know what is and is not possible for experimentalists. You might not like it, but that's what makes it science vs. pure math.
  10. Nov 14, 2007 #9
    I recall a certain story about NASA trying to place an order for a gram of antimatter...:rolleyes:
  11. Nov 14, 2007 #10
    I thought only Dan Brown was that dumb? :rolleyes:

    I agree with the point Poop-Loops is making about the importance of experiment... but is it strictly necessary as part of an undergrad course?
    My physics tutor researches now in astrophysics and cosmology, and I found out yesterday his undergrad degree was single honours maths; he picked up all the experimental stuff as part of his PhD and on the job.

    And I'm afraid that computer programming is something you really have to come to terms with as a physicist. Experimentalists use programs to control sensitive equipment and analyse complex data; theorists use them to do hard math! If you haven't started university yet this idea might seem really strange to you, but there are some calculations it's pretty well impossible to do analytically; think for a few minutes about trying to describe in general the motion of 4 planets due to each other's gravity if you don't believe me :biggrin: Big computers get around this problem by breaking it down into small sums that numerically approximate the calculus very well indeed.
  12. Nov 14, 2007 #11


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I think experiment should part of an undergrad [and high-school] physics course-of-study. Certainly, one can try to avoid the experimental part by pursuing another course-of-study.. like mathematics... [even though one could find a job in physics research]. But a physics course-of-study is incomplete without some experimental work.
  13. Nov 14, 2007 #12
    I really wouldn't worry about it. I know many math/phys people who don't love CS but had to take a first year course. Most of them (including myself) enjoyed it and did well. It's really not too hard of a class especially for a mathematically minded person (my opinion), if fact I would say it's relativly easy. I liked it enough that I'll do a minor or concentration in CS. It complements math/phys quite well (maybe more so math i dunno)
  14. Nov 14, 2007 #13
    As a physics course it's certainly incomplete.
    It is, however, probably worthwhile pointing out the distinction between theoretical and mathematical physics. Theoretical physics uses advanced mathematical techniques to formulate models to try predict the results of experiment, and to describe nature in terms of a mathematical formalism (sometimes with scant regard for the current advancement of experimental technique in a particular area). Mathematical physics, meanwhile, focuses more on maths as a subject in its own right, with more rigourous standards of proof expected. Mathematical and theoretical physicists work on the same material, and probably enjoy their jobs for the same reasons as each other, but there are occasions where the distinction is important (see here for example). I suspect that rigour on the level of mathematical physics would be hard to come by in a normal undergrad physics degree, so it's worthwhile axiom-dt thinking about whether or not he cares if he's employed within a physics or a maths department :biggrin:
  15. Nov 14, 2007 #14
    But there is no real 'Theoretical Physics' undergraduate program is there? Mathematical physics is still the most appropriate undergraduate program for someone in my position, right?

    And thank you to all who took time to respond, if lab experience and knowledge of computer science are important in determining how successful I am then I won't shy away from them.

    Taking mathematical physics through the faculty of math appeals more to me than taking it through the faculty of science because I get the impression that a Bachelor of Math degree looks better and more distinguishing than a Bachelor of Science - please correct me if my superficial reasoning is completely wrong.
  16. Nov 14, 2007 #15
    Not really, since the University of Waterloo is the only university in North America that has a Faculty of Mathematics.

    The University of Toronto's "Math and Physics Specialist" program is offered through the Mathematics Department, btw. The only lab courses you have to take in that program are in the freshman introductory course and the sophomore Physics Laboratory course. All other Physics people have to take more labs.
  17. Nov 14, 2007 #16
    Consider yourself corrected :tongue:
    It's generally accepted that good degrees in maths or in physics aren't easy to come by, so I'd say it's only worth considering how much you will enjoy each degree and how well it prepares you for a PhD (if that is your ultimate aim).

    I know nothing about Canadian universities, but in the UK theoretical physics degrees are more common than mathematical physics degrees. There's also the joint honours maths and physics option to consider (which is what I do.)
  18. Nov 14, 2007 #17
    Physics is a science. It needs experiments to be one.
    Do I really need to take computer science classes for a computer science degree? I can pick all that up on the job.

    That's pretty much my argument. I mean, even the grad students and post-docs I worked with over the summer said that going into grad school (these are all experimentalists, by the way) they didn't know much about electronics and stuff like that, but they picked it up by osmosis.

    HOWEVER! You need to know how to write up a lab report. Know some rudimentary error analysis. How experiments are set up, etc.

    I mean, you can learn all that on your own, but if you don't want to take a class on it, what makes you think you'll put in the effort to learn it on your own?
  19. Nov 14, 2007 #18
    I thought that 'Theoretical Physics', 'Mathematical Physics', and 'Joint Honours Math and Physics' were synonymous when speaking in terms of university undergraduate degrees..

    Glancing at some of the Canadian university sites, most of them have 'Joint Math and Physics' and nothing else, Waterloo just happens to call it 'Mathematical Physics' but it is still offered jointly by the departments of Applied Math and Physics. The only program close to being called Theoretical Physics is McMaster's 'Computation and Theory' program under the department of physics.

    The descriptions for these programs usually mention them being 'optimized for theoretical physics'.. am I missing something here?
  20. Nov 14, 2007 #19
    Firstly, let me point out that I chose a course where I would be forced to do these things! Secondly, you can pick up points of technique of this nature from scratch much faster than you can pick up the collective theoretical frameworks of, say, quantum mechanics, classical electromagnetism and special relativity :rolleyes: I do think you're better off studying these things as an undergraduate, but it's not going to be a nightmare to acquire these skills (and applying them to more interesting physics than the crap they give you as a first year undergrad :rolleyes:) in a further course of study. So they're undeniably important, and extremely useful to master as an undergrad, but not *strictly essential* at a UG level. So if our friend wasn't sure if he wanted to do research or not, hates labs and wants to make sure he enjoys his degree, then he should be aware of the possibility of entering this field of research without any deal of experimental background. Plenty of people do it, including cristo from these forums if you want more info axiom_dt.

    Theoretical physics is certainly not synonymous with Joint honours maths and physics; it's just likely that your maths options in the later years of the latter will be on applied topics like fluid dynamics or general relativity. But you shouldn't neglect that in the JH degree maths will be presented as a subject in its own right, by people who usually research it it for its own sake, rather than as a tool for physicists. A theoretical physics course is likely to have more maths and less labwork than a standard physics degree, but that maths is still likely to be taught from a "toolbox" rather than a necessarily rigourous perspective. The upshot is that it's tailored to what is relevant to physics, without digressions into topics like number theory.
  21. Nov 14, 2007 #20
    This is alarming, I can't even find an UG program entitled 'Theoretical Physics', only 'Joint Math and Physics' or, more rarely, 'Mathematical Physics..

    What are the differences between these programs?

    Let me just say that I enjoy math in its own right, I don't see it as merely a tool and definitely would not mind going into pure math. However, I find physics at the fundamental level so important and so interesting that I cannot pass up the opportunity of spending my life attempting to get answers to deep questions about the universe.

    With that in mind, what is the undergraduate degree for me? If theoretical physics is not offered anywhere as a UG degree then what is its equivalent?

    Thanks again for taking time to help me with these matters.
  22. Nov 15, 2007 #21
    If you really know that you want to research, then it almost doesn't matter; any of these degrees would give you what you needed to undertake a PhD. Beyond a few provisos already outlined (like labs and programming being good ideas) pick one you think you'll enjoy from a university you fancy going to.
  23. Nov 15, 2007 #22
    I completely agree,
    tell me if I'm wrong but I think many of these posts are over emphasizing the differences between the various undergrad physics majors.

    In my opinion they are all fairly the same they just differ in a few lab classes, and the amount and / or rigor of the maths you take.

    For example, a regular physics degree will have you take calc 1-3 + Diff EQ and probably a math methods class for some partial diff eq's, integration techniques, a little Fourier analysis.
    Then you will also take 4 or 5 maybe 5 or 6 lab classes.

    Where as Theo Physics will substitute the lab classes for more Theory based physics classes like advanced classical mechanics, EM II, Advanced Quantum... As well as give you more math depth, like requiring Linear and Linear II, Abstract Algebra, Real Analysis

    If you find a school with a Mathematical Physics Degree, I think it will be very similar to general Theo Physics degree I just tried to describe. Same with the Joint Physics and Maths, with that degree you probably take even more maths to satisfy both a physics and a math major.

    Thus I think there is not too much difference, like muppet said, If you plan on Grad School, or doing Research, any of those degrees will prepare you for grad classes and research methods.
  24. Nov 15, 2007 #23


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I agree.
    I would put more emphasis on who my professors would be [what they do research on and how well they teach and write], the scientific activity and reputation of the department and university, and the quality of the facilities [labs, depth-of-library, computational resources, etc..].
  25. Nov 15, 2007 #24
    I agree with this. Maybe too much emphasis is being placed on what the undergrad degree is, as opposed to how well you do in it.

    A note to those going into theory though: the field is really, really crowded. The number of very good theorists being produced throughout the world outnumbers the jobs available by a tremendous amount. You'll be up against the very top few percent coming from very populous countries.

    There will be no room for missteps! Get in a good undergraduate program (worry more about the school than the name of the program) and nail it. Then repeat for masters, phd, and your next 4 postdoc positions.
  26. Nov 15, 2007 #25
    Hmm, do you know how crowded exactly? Do you have a statistical reference or is it just hearsay? I am very prepared to compete but not if it is the equivalent of trying to find a job with a philosophy degree.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook